Another Equal Valued Active LPF

[mawyatt]

This circuit reminded me of the active ripple filter for a high-voltage power supply that I once designed. This circuit, similarly, connects thru two capacitors to the amplifier. Thanks to this, the low-voltage amplifier can suppress ripple at high voltage. I was wondering if the 3rd order filter presented in the topic can be used for power supply filtration, but it seems that it is not possible because the low series resistance R causes an increase in quality factor.

The circuit shown has no DC feedback to the op-amp inverting input. This will cause the op-amp output to saturate.

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[mawyatt]

Here's an interesting variation, a very simple single transistor version of a DC Accurate 3rd Order Butterworth LPF approximation. Around the -3dB transition region it's not as good as a op-amp based due to gain limitations, however has better stop band attenuation and can handle bipolar input voltages even though it's only single supply VCC biased.

Here's some LTspice simulations of Ideal, Op-Amp based, and Single Transistor versions. We also cobbled together a protoboard with an 2N3904 we had laying around and included the Op-Amp (OP07) version for comparisions.

Anyway, hope some find this single transistor version interested

[RoGeorge]

Wow, only one transistor, that's quite a surprise! 

And the circuit with BJT has a 10dB better rejection above 10kHz than the opamp one! 
Is this because OP07 is too slow?  I wonder if the rejection would improve with a faster opamp.

[David Hess]

Wow, only one transistor, that's quite a surprise! 

And the circuit with BJT has a 10dB better rejection above 10kHz than the opamp one! 
Is this because OP07 is too slow?  I wonder if the rejection would improve with a faster opamp.

The output impedance of the OP-07 is its open loop output impedance divided by the circuit's loop gain, which is the gain in excess of the closed loop gain.  As the open loop gain decreases with frequency, the loop gain also falls, and so the output impedance increases.

The usual solution is to add a buffer to the OP-07 within the feedback loop to lower its output impedance, which is not demanding because the OP-07 is slow.  This could be a discrete transistor buffer, integrated buffer like an LT1010, or a fast voltage or current feedback follower.  In some cases an RC filter can be added to the output to provide a low AC impedance at high frequency, or if the operational amplifier can drive capacitive loads, just the capacitor.

For the single transistor version, it is common in discrete circuits to see a variation of a Sziklai pair instead to provide even lower output impedance.  This is especially the case when the input transistor is a JFET.

[Circlotron]

Just for fun I tried that 3 opamp filter using emitter followers instead of opamps. PN100s with a 1K source resistor. Not DC accurate anymore, but the rolloff really gets with it! Keeps on going down to 90kHz. 4V input becomes 10uV @ 90kHz.

[mawyatt]

Just for fun I tried that 3 opamp filter using emitter followers instead of opamps. PN100s with a 1K source resistor. Not DC accurate anymore, but the rolloff really gets with it! Keeps on going down to 90kHz. 4V input becomes 10uV @ 90kHz.

The triple emitter follower certainly works, this was used in a radar detector long ago where DC and low frequency accurate amplitude response didn't matter. Vaguely recall this approach results in something similar to a Bessel amplitude response.

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[mawyatt]

Wow, only one transistor, that's quite a surprise! 

And the circuit with BJT has a 10dB better rejection above 10kHz than the opamp one! 
Is this because OP07 is too slow?  I wonder if the rejection would improve with a faster opamp.

Yes, we thought this quite interesting and not intuitively obvious, so decided to post!!

Of course using a faster op-amp will help with stop band rejection (OP07s are slow). Look at the plots and you can see how the OP07 stop band plateaus after 10kHz. This is because the output impedance is inductive, rising with frequency, and being somewhat countered by the filter capacitive roll off. We've commented and shown this behavior a few times in various threads. Some op amps (LM358/324 types) can be improved by simply adding a shunt bias bleed current resistor to VEE (or VCC) to force the output into a somewhat Class A mode (Emitter Follower) with a lower output Z. You also can add an external buffer or emitter follower for a lower effective output Z.

Somewhere way back in the 80s we published a Design Idea in EDN on this after being asked to investigate a microwave synthesizer broadband noise performance and discovered the op-amp based active LPF and driver to the YIG oscillator were limiting the stop band attenuation to the high speed control port on the YIG (these had dual control ports, one high speed limited range the other low speed wide range). A couple strategically placed resistors solved the problem for the customer demo. Later a redesign just used faster op-amps.

Best 

[mawyatt]

Just for fun I tried that 3 opamp filter using emitter followers instead of opamps. PN100s with a 1K source resistor. Not DC accurate anymore, but the rolloff really gets with it! Keeps on going down to 90kHz. 4V input becomes 10uV @ 90kHz.

Here's a version using complementary emitter followers that is somewhat DC accurate with ~30mV offset. The amplitude response is somewhere between a Butterworth and Bessel as shown in simulations, however the phase response is almost identical to the Butterworth in the range shown. We included a DC Accurate (op-amp) and Sallen-Key for comparison and even did some Bode measurements of such, including the single transistor version

All these filters use the same 10kΩ and 0.01uF for the frequency determining elements which places the "corner" frequency at 10krad/s (1.59kHz).

BTW the sim "E" VCVS sources are included to allow normalizing the gain of all the LPFs to the Emitter Follower gain which is ~0.9 as shown.

Anyway, just another version of these filters, hopefully other's will find this stuff interesting.

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[mawyatt]

Even another variation of the 3rd Order Equal Value Component Sallen-Key type, which has a gain of 2X. This simply implements a:

2/[(S^2 + S +1)(S + 1)] or 2/[S^3 + 2S^2 + 2S +1] Transfer Function.

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[mawyatt]

Swapping the Rs and Cs translates to a 3rd Order Butterworth High Pass Filter, still with Equal Valued Components, even for the Emitter Follower type. Here's some simulations and actual measurements of the Sallen-Key, Sallen-Key-2 and Emitter Follower.

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[MT4S301]

I build the active LPF with discrete BJTs without doing any transfunc calculation.
Sadly it turns out the OPAMP in this topology cannot simply directly be replaced by a transconductor
Finally got the butterworth response after I unwillingly add an EF stage that I want to avoid (for complexity, power, stability reasons)

[mawyatt]

I build the active LPF with discrete BJTs without doing any transfunc calculation.
Sadly it turns out the OPAMP in this topology cannot simply directly be replaced by a transconductor
Finally got the butterworth response after I unwillingly add an EF stage that I want to avoid (for complexity, power, stability reasons)

This topology is generally not intended for higher frequency use, mostly delegated to DC and low frequency where DC accuracy is paramount (filtering references for example). As you move up in frequency as you've shown this requires higher gain @ frequency (GBWP) while maintaining a low output Z for stop band rejection.

If you take the complexity of your 3 transistor circuit to achieve a reasonable approximation to a 3rd Order Butterworth function at ~500kHz, this illustrates the need for the extended GBWP active elements and begins to make this particular Butterworth topology unfavorable for discrete active devices. A simple passive LC filter should suffice (with reasonable L values) if the intent is actual use rather than intellectual curiosity.

Anyway, it's nice to see you looking into this topology, hopefully others will also

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[MT4S301]

This topology is generally not intended for higher frequency use, mostly delegated to DC and low frequency where DC accuracy is paramount (filtering references for example)... simple passive LC filter should suffice (with reasonable L values) if the intent is actual use rather than intellectual curiosity.

I totally understand its intended use (as reference buffers) but its "bias irrelevant" character intrigue me into finding other application for the topology.
The first scenario that come to my mind is homemade transistor radio where there's always too many components. Such LPF may offer fast rolloff for IF/baseband with fewest parts required and avoid bulky inductors that make a <1MHz LPF

[mawyatt]

The first scenario that come to my mind is homemade transistor radio where there's always too many components. Such LPF may offer fast rolloff for IF/baseband with fewest parts required and avoid bulky inductors that make a <1MHz LPF

If you want to have some fun with radio receivers, take a look at this thread about the PolyPhase Mixer. A couple decades ago this physics defying passive mixer concept (NF below theoretical) created a whirlwind in academia

https://www.eevblog.com/forum/rf-microwave/polyphase-or-n-path-mixer/msg5753297/#msg5753297

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[mawyatt]

The DC Accurate version of the 3rd Order Butterworth LPF can be reconfigured into a High Pass just like the other versions presented, and also uses equal valued Rs and Cs. Of course the HP version is no longer a "DC Accurate" type since the output involves resistor connections to the op-amp input and output, thus presenting a finite small offset.

Here's a simulation (included ideal response) and actual measurement based upon an OP07, agrees well with the Simulation and Idea Response.

Anyway, another version to have some fun with.

Best